Hi Suziq,
Here they are wrongly enumerated as TIMONS.
1841. HO/107/1354 Folio 8 Page 8
York St Margaret
Walmgate
Rosemary Place.
William Timons 30 Basket Maker Y
Hannah " 25 Y
George " 5 Y
William " 10mths Y
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As a bounus here is the 1851 census.
Address as above.
Hannah Timons Head Mar 34 Yarm Yks
George " son 13 Appleton Yks
William " son 11 York Yks
Charles " son 1 York Yks
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No trace of William on the 1851 in York
Trevor